Arianna appeared as a guest on ABC's "This Week" on Sunday, along with Liz Cheney, Markos Moulitsas, and George Will.

Arianna squared off with Cheney over the Gulf oil disaster, calling out the Bush-Cheney administration for its role in fostering the crisis.

"The truth is that right now we have precisely the regulatory system that the Bush-Cheney administration wanted: full of loopholes, full of cronies and lobbyists filling the very agencies that are supposed to be overseeing the industry," Arianna said. "We are seeing this as the inevitable result of what they wanted."

"It is truly amazing," Cheney responded. "I actually heard that George Bush was responsible for the breakup of Tipper and Al Gore's marriage, too. It's incredible, the extent to which people are now trying to shift blame. ... The left -- you guys have for years been demonizing Bush and Cheney, and I'm sure you’ll be demonizing them for years going forward. But we have a catastrophe on the Gulf coast, a catastrophe that happened on this administration's watch, which this administration is failing to clean up."

"We have the poster child of Bush-Cheney crony capitalism, Halliburton, involved in this," Arianna said. "They, after all, were responsible for cementing the well. Here's Halliburton, after it defrauded the American taxpayer hundreds of millions of dollars -- "

"I don't know what planet you live on," Cheney shot back. "What you are saying has no relationship to the truth, no relationship to the facts."

"I live on this planet," Arianna said. "Halliburton was involved in this. How can you say there is no relationship?"

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Cheney also addressed the Israeli raid on the Gaza aid flotilla, and conceded that it was a mistake for the Bush administration to push for the 2006 Palestinian elections.

"You were at the State Department in 2005, 2006 when these [Palestinian] elections were pushed," host Jake Tapper said. "And some people were saying 'Don't do it, they're not ready for it.' Do you think that was a mistake in retrospect?"

"I do," Cheney replied. "I don't think they were ready for it. I don't think we should have pushed it."